15 citations · 17 across the 13 of their papers we have counts for
6 papers · 1 filter
Surface Wave Solutions in 1D and 2D for the Broer-Kaup-Boussinesq-Kupershmidt (BKBK) System
Darryl D. Holm, Ruiao Hu, Hanchun Wang
The BKBK system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification int…
A Multiscale Camassa--Holm Equation
Darryl D Holm, Maneesh Kumar Singh
A system of equations for Multiscale Geodesic Flow (MGF) is introduced whose solutions illustrate the paradigm of whorls within whorls within whorls, introduced by L. F. Richardson…
A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations
Darryl D. Holm, Maneesh Kumar Singh, Oliver D. Street
We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a comple…
Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
Darryl D. Holm, Ruiao Hu, Oliver D. Street +1
We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water.…
A thermal Green-Naghdi model with time dependent bathymetry and complete Coriolis force
Darryl D. Holm, Oliver D. Street
This paper extends the theoretical Euler-Poincaré framework for modelling ocean mixed layer dynamics. Through a symmetry-broken Lie group invariant variational principle, we derive…
Plasma dynamics in thin domains
Darryl D. Holm, Ruiao Hu, Oliver D. Street
In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincaré variation…